Problem: What do the following two equations represent? $-3x+5y = 2$ $-10x-6y = 4$
Answer: Putting the first equation in $y = mx + b$ form gives: $-3x+5y = 2$ $5y = 3x+2$ $y = \dfrac{3}{5}x + \dfrac{2}{5}$ Putting the second equation in $y = mx + b$ form gives: $-10x-6y = 4$ $-6y = 10x+4$ $y = -\dfrac{5}{3}x - \dfrac{2}{3}$ The slopes are negative inverses of each other, so the lines are perpendicular.